Sudoku rules

Sudoku is a 9×9 number puzzle divided into nine 3×3 boxes. Fill every cell with a digit from 1 to 9 so that each row, each column, and each 3×3 box contains every digit exactly once. The puzzle starts with some cells already filled (called “givens”); your task is to deduce the remaining digits using logic alone - no guessing is needed for a well-formed puzzle.

Difficulty levels and givens

Difficulty	Approximate givens	Techniques required
Easy	~36–38	Naked singles only
Medium	~30–32	Hidden singles
Hard	~24–26	Pointing pairs, naked/hidden pairs
Expert	~20–22	X-wing, XY-wing, chains

Core solving strategies

Naked single: a cell has only one digit that can legally go there. This is the simplest technique and fills most cells in easy puzzles.
Hidden single: within a row, column, or box, one digit has only one possible cell - even if that cell still has multiple candidates.
Naked pair: two cells in the same unit share exactly the same two candidates. Those two digits can be eliminated from all other cells in that unit.
Pointing pair/triple: if a digit’s candidates in a box all fall within the same row or column, that digit can be eliminated from the rest of that row or column outside the box.
X-wing: if a digit appears in exactly two cells in each of two rows, and those cells share the same two columns, then that digit can be eliminated from the rest of those columns.

Solving strategy progression

Techniques in order of increasing difficulty - work through them in sequence when you get stuck:

Naked singles: only one digit fits in the cell.
Hidden singles: only one cell in a unit can hold a particular digit.
Naked pairs/triples: two/three cells share the same two/three candidates.
Pointing pairs: candidates in a box confined to one row or column.
X-wing: a digit locked to two rows and two columns simultaneously.
Swordfish: like X-wing but spanning three rows and three columns.
Forcing chains / bifurcation: last resort - assume a candidate and follow consequences.

How the puzzle is generated

The generator starts by filling a complete valid 9×9 grid (which can be done quickly by solving an empty board with the backtracking algorithm). It then removes clues one at a time, checking after each removal that the puzzle still has exactly one valid solution. Clues are removed symmetrically (180° rotational symmetry) for aesthetic reasons. This process continues until the target number of givens is reached for the chosen difficulty level.

Daily puzzle challenge

Many sudoku enthusiasts treat the puzzle as a daily mental exercise. Consider printing one Expert-level puzzle per week as a focused challenge - solving on paper without hints builds stronger pattern recognition than solving digitally. Newspaper sudoku puzzles are graded by day of the week, with Monday being easiest and Saturday the hardest.